We present a Matlab program that computes infinite range integrals of an arbitrary product of Bessel functions of the first kind. The algorithm uses an integral representation of the upper incomplete Gamma function to integrate the tail of the integrand. This paper describes the algorithm and then focuses on some implementation aspects of the Matlab program. Finally we mention a generalisation ...

Change in impedance of an encircling coil is obtained in the present paper for the case where the electric conductivity and magnetic permeability of a metal cylindrical tube depend on the radial coordinate. The system of equations for the vector potential is solved by means of the Fourier cosine transform. The solution is expressed in terms of improper integral containing modified Bessel functi...

In this work, we extend the analytic treatment of Bessel functions of large order and/or argument. We examine uniform asymptotic Bessel function expansions and show their accuracy and range of validity. Such situations arise in a variety of applications, in particular the Fourier transform of the gravitational wave signal from a pulsar. The uniform expansion we consider here is found to be vali...

The connection between the Bessel discrete variable basis expansion and a specific form of an orthogonal set of Jacobi polynomials is demonstrated. These so-called Zernike polynomials provide alternative series expansions of suitable functions over the unit interval. Expressing a Bessel function in a Zernike expansion provides a straightforward method of generating series identities. Furthermor...